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On commutativity of rings with some polynomial constraints

Published online by Cambridge University Press:  17 April 2009

Mohd Ashraf  and
Murtaza A. Quadri
Mohd Ashraf
Affiliation:
Department of MathematicsAligarh Muslim UniversityAligarh 202 002India
Murtaza A. Quadri
Affiliation:
Department of MathematicsAligarh Muslim UniversityAligarh 202 002India
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Abstract

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Let R be an associative ring with unity 1, N(R) the set of nilpotents, J(R) the Jacobson radical of R and n > 1 be a fixed integer. We prove that R is commutative if and only if it satisfies (xy)n = ynxn for all x, y ∈ R \ N(R) and commutators in R are n(n + 1)-torsion free. Moreover, we extend the same result in the case when x, y ∈ R\J(R).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 201 - 206
Copyright
Copyright © Australian Mathematical Society 1990

References

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